Structuralism, indiscernibility, and physical computation.
Structuralism about mathematical objects and structuralist accounts of physical computation both face indeterminacy objections. For the former, the problem arises for cases such as the complex roots i and - i , for which a (non-trivial) automorphism can be defined, thus establishing the structural i...
| Publicado en: | Synthese Vol. 200; no. 3; pp. 1 - 27 |
|---|---|
| Autores principales: | , |
| Formato: | Artículo |
| Publicado: |
Springer Nature
Jun2022
|
| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=156560806&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 156560806 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Jun2022 vid: 200 iid: 3 pid: 237 pub: Springer Nature artinfo: ui: 156560806 10.1007/s11229-022-03691-1 ppf: 1 ppct: 26 formats: fmt: – @attributes: type: T – @attributes: type: P size: 401KB tig: atl: Structuralism, indiscernibility, and physical computation. aug: au: Doherty, F. T. Dewhurst, J. affil: Independent scholar, Glasgow, Scotland LMU Munich, Munich, Germany sug: keyword: Computation Hilbert Indeterminacy Indiscernibility Structuralism ab: Structuralism about mathematical objects and structuralist accounts of physical computation both face indeterminacy objections. For the former, the problem arises for cases such as the complex roots i and - i , for which a (non-trivial) automorphism can be defined, thus establishing the structural identity of these importantly distinct mathematical objects (see e.g. Keränen in Philos Math 3:308–330, 2001). In the case of the latter, the problem arises for logical duals such as AND and OR, which have invertible structural profiles (see e.g. Shagrir in Mind 110(438):369–400, 2001). This makes their physical implementations indeterminate, in the sense that their structural profiles alone cannot establish whether a given physical component is an AND-gate or an OR-gate. Doherty (PhilPapers, , 2021) has recently shown both problems to be analogous, and has argued that computational structuralism is threatened with the absurd conclusion that computational digits might be indiscernible, such that, if structural properties are all that we have to go on, the binary digit 0 must be treated as identical to the binary digit 1 (rendering pure structuralism absurd). However, we think that a solution to the indiscernibility problem for mathematical structuralists, drawing on the work of David Hilbert, can be adapted for the analogous problem in the computational case, thereby rescuing the structuralist approach to physical computation. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2022. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2022 holdings: @attributes: islocal: N |
|---|